iPad Air/iOS 7.0.6:
iPhone 4s/iOS 7.0.6:
Nexus 7 (original model, Android KitKat):
Incidentally, I have previously flagged this problem via the in-page 'report a problem' facility (around, or slightly before, 17/02/2014) and received this response:
Thanks for showing your interest in this position: http://careers.stackoverflow.com/jobs/485341
You should be able to see the "apply now" button at the bottom of this job listing. Can you try a different browser if you aren't able to see that?
(Name removed, since I don't think it's fair to potentially embarrass someone)
1: Note that this is an entirely different job, though it shows the same behaviour.